The Magid Mishneh (Shabbas 29, 18) states that no source exists that Kiddush on Yom Tov is from the Torah. He brings no source for his view, and there are sources that indicate the opposite.
The Mechilta (Parshas Emor) states זכור את היום השבת לקדשו implies that we make the day holy with a blessing (over wine). How do we know that this also includes Yom Tov, as it says “These are the Holidays” (VaYikra 23,2). The reason we include Yom Tov from this text is that the text continues with Shabbos (23, 3). Thus, the laws of Shabbos apply equally to Yom Tov, unless the Torah makes a difference (for example, the laws of food preparation).
In addition, the Kiddush of the holiday of Rosh HaShana has a further source. The Gemara (Rosh HaShana 35a) cites the verse (VaYikra 23, 24) שבתון זכרון תרועה מקרא קודש which is in the middle of the section of Rosh HaShana. Rabbi Eliezer says שבתון indicates the sanctification of the day (making Kiddush) and מקרא קודש indicates the sanctification that occurs by refraining from melacha. Rabbi Akiva says שבתון indicates the sanctification that occurs by refraining from melacha and מקרא קודש indicates the sanctification of the day (making Kiddush). Both Rabbis learn that Kiddush on Rosh HaShana is from the Torah.
In addition, the law follows Rabbi Akiva. And he derives Kiddush on Rosh HaShana from the phrase מקרא קודש this would apply to all the other Yom Tovim since they also have the phrase מקרא קודש.
This matter is a great wonder since the Lechem Mishneh and the Mogen Avrohom both rely on the opinion of the Magid Mishneh, which seems without a source. This needs further clarification.
